A debtor files bankruptcy to discharge his obligations and relieve himself of responsibility for paying them. If you have an open line of credit or a credit card with a zero balance, this isn't a debt. You don't owe anything, so you're not under any legal duty to include it in your bankruptcy petition. However, whether it will be there waiting for you when you come out on the other side of the proceedings is another matter.
The Trustee's Position
If your account has no balance because you paid more than $600 toward it in the three months right before you filed for bankruptcy, you might have a problem. You must report this activity to your trustee, who can demand that the creditor return the money. It would then go into your bankruptcy estate for distribution among all your creditors so that they're all treated equally.
If you file for chapter 13, you cannot use available credit while you're in bankruptcy as you're prohibited from incurring any new debt until after you receive your discharge. The creditor might cancel your account anyway, whether you file for chapter 7 or chapter 13 protection. Creditors regularly check bankruptcy filings to make sure their customers' names don't turn up. If your name does, the creditor can close your account rather than take the risk of extending you credit after your bankruptcy is over.